194,637 research outputs found
Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis
In this paper, we consider a regression model built on dependent variables.
This regression modelizes an input output relationship. Under boundedness
assumptions on the joint distribution function of the input variables, we show
that a generalized Hoeffding-Sobol decomposition is available. This leads to
new indices measuring the sensitivity of the output with respect to the input
variables. We also study and discuss the estimation of these new indices
Where Does the Density Localize? Convergent Behavior for Global Hybrids, Range Separation, and DFT+U
Approximate density functional theory (DFT) suffers from many-electron self-
interaction error, otherwise known as delocalization error, that may be
diagnosed and then corrected through elimination of the deviation from exact
piecewise linear behavior between integer electron numbers. Although paths to
correction of energetic delocalization error are well- established, the impact
of these corrections on the electron density is less well-studied. Here, we
compare the effect on density delocalization of DFT+U, global hybrid tuning,
and range- separated hybrid tuning on a diverse test set of 32 transition metal
complexes and observe the three methods to have qualitatively equivalent
effects on the ground state density. Regardless of valence orbital diffuseness
(i.e., from 2p to 5p), ligand electronegativity (i.e., from Al to O), basis set
(i.e., plane wave versus localized basis set), metal (i.e., Ti, Fe, Ni) and
spin state, or tuning method, we consistently observe substantial charge loss
at the metal and gain at ligand atoms (ca. 0.3-0.5 e or more). This charge loss
at the metal is preferentially from the minority spin, leading to increasing
magnetic moment as well. Using accurate wavefunction theory references, we
observe that a minimum error in partial charges and magnetic moments occur at
higher tuning parameters than typically employed to eliminate energetic
delocalization error. These observations motivate the need to develop
multi-faceted approximate-DFT error correction approaches that separately treat
density delocalization and energetic errors in order to recover both correct
density and magnetization properties.Comment: 34 pages, 11 figure
Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations
To perform uncertainty, sensitivity or optimization analysis on scalar
variables calculated by a cpu time expensive computer code, a widely accepted
methodology consists in first identifying the most influential uncertain inputs
(by screening techniques), and then in replacing the cpu time expensive model
by a cpu inexpensive mathematical function, called a metamodel. This paper
extends this methodology to the functional output case, for instance when the
model output variables are curves. The screening approach is based on the
analysis of variance and principal component analysis of output curves. The
functional metamodeling consists in a curve classification step, a dimension
reduction step, then a classical metamodeling step. An industrial nuclear
reactor application (dealing with uncertainties in the pressurized thermal
shock analysis) illustrates all these steps
Finite-frequency sensitivity of body waves to anisotropy based upon adjoint methods
We investigate the sensitivity of finite-frequency body-wave observables to mantle anisotropy based upon kernels calculated by combining adjoint methods and spectral-element modelling of seismic wave propagation. Anisotropy is described by 21 density-normalized elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. In a 1-D reference model, body-wave sensitivity to anisotropy is characterized by ‘banana–doughnut’ kernels which exhibit large, path-dependent variations and even sign changes. P-wave travel-times appear much more sensitive to certain azimuthally anisotropic parameters than to the usual isotropic parameters, suggesting that isotropic P-wave tomography could be significantly biased by coherent anisotropic structures, such as slabs. Because of shear-wave splitting, the common cross-correlation travel-time anomaly is not an appropriate observable for S waves propagating in anisotropic media. We propose two new observables for shear waves. The first observable is a generalized cross-correlation travel-time anomaly, and the second a generalized ‘splitting intensity’. Like P waves, S waves analysed based upon these observables are generally sensitive to a large number of the 21 anisotropic parameters and show significant path-dependent variations. The specific path-geometry of SKS waves results in favourable properties for imaging based upon the splitting intensity, because it is sensitive to a smaller number of anisotropic parameters, and the region which is sampled is mainly limited to the upper mantle beneath the receiver
Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models
Global sensitivity analysis aims at quantifying the impact of input
variability onto the variation of the response of a computational model. It has
been widely applied to deterministic simulators, for which a set of input
parameters has a unique corresponding output value. Stochastic simulators,
however, have intrinsic randomness due to their use of (pseudo)random numbers,
so they give different results when run twice with the same input parameters
but non-common random numbers. Due to this random nature, conventional Sobol'
indices, used in global sensitivity analysis, can be extended to stochastic
simulators in different ways. In this paper, we discuss three possible
extensions and focus on those that depend only on the statistical dependence
between input and output. This choice ignores the detailed data generating
process involving the internal randomness, and can thus be applied to a wider
class of problems. We propose to use the generalized lambda model to emulate
the response distribution of stochastic simulators. Such a surrogate can be
constructed without the need for replications. The proposed method is applied
to three examples including two case studies in finance and epidemiology. The
results confirm the convergence of the approach for estimating the sensitivity
indices even with the presence of strong heteroskedasticity and small
signal-to-noise ratio
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